The exact solution of systems of linear equations with polynomial coefficients
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Mcclellan, M. T.↗
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Results for “EXACT SOLUTIONS”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Random function theory revisited - Exact solutions versus the first order smoothing conjecture
We remark again that the mathematical conjecture known as first order smoothing or the quasi-linear approximation does not give the correct dependence on correlation length (time) in many cases, although it gives the correct limit as the correlation length (time) goes to zero. In this sense, then, the method is unreliable.
Lerche, I.↗
Exact solution of some linear matrix equations using algebraic methods
A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.
Djaferis, T. E.↗
Exact solutions in oscillating airfoil theory
A result obtained by Williams (1977) for two-dimensional airfoils oscillating in an arbitrary subsonic parallel flowfield is reformulated to show that the pressure distribution induced by any deformation can be construed from the particular solutions for heaving and pitching motions. Specific formulas are presented for an oscillating control surface with a sealed gap.
Williams, M. H.↗
Magnetohydrodynamic equilibrium. I - Exact solutions of the equations
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Tsinganos, K. C.↗
Exact solutions for sporadic acceleration of cosmic rays
The steady state spectra of cosmic rays which are subject to a sporadic acceleration process, wherein the gain in energy in each encounter is a finite fraction of the particle energy are discussed. They are derived from a mathematical model which includes the possibility of energy dependent leakage of cosmic rays from the galaxy. Comparison with observations allows limits to be placed on the frequency and efficiency of such encounters.
Cowsik, R.↗
An exact solution for the solidification of a liquid slab of binary mixture
The time dependent temperature and concentration profiles of a one dimensional finite slab of a binary liquid alloy is investigated during solidification. The governing equations are reduced to a set of coupled, nonlinear initial value problems using the method outlined by Meyer. Two methods will be used to solve these equations. The first method uses a Runge-Kutta-Fehlberg integrator to solve the equations numerically. The second method comprises of finding closed form solutions of the equations.
Antar, B. N.↗
Exact solution of three-dimensional transport problems using one-dimensional models
Several parameters of certain three-dimensional semiconductor devices including diodes, transistors, and solar cells can be determined without solving the actual boundary-value problem. The recombination current, transit time, and open-circuit voltage of planar diodes are emphasized here. The resulting analytical expressions enable determination of the surface recombination velocity of shallow planar diodes. The method involves introducing corresponding one-dimensional models having the same values of these parameters.
Misiakos, K.↗
Some exact solutions of two-dimensional flows of compressible fluid with hodograph method
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Chang, Chien-Chien↗
Exact solutions of laminar-boundary-layer equations with constant property values for porous wall with variable temperature
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HEAT TRANSFER, AERODYNAMIC↗
On a class of exact solutions of the equations of motion of a viscous fluid
The general solution is obtained of the equations of motion of a viscous fluid in which the velocity field is inversely proportional to the distance from a certain point. Some particular cases of such motion are investigated.
FLOW, LAMINAR↗
Comparison of exact solution with Eikonal approximation for elastic heavy ion scattering
A first-order optical potential is used to calculate the total and absorption cross sections for nucleus-nucleus scattering. The differential cross section is calculated by using a partial-wave expansion of the Lippmann-Schwinger equation in momentum space. The results are compared with solutions in the Eikonal approximation for the equivalent potential and with experimental data in the energy range from 25A to 1000A MeV.
Dubey, Rajendra R.↗
Magnetically driven jets and winds: Exact solutions
We present a general class of self-similar solutions of the full set of MHD equations that include matter flow, electromagnetic fields, pressure, and gravity. The solutions represent axisymmetric, time-independent, nonrelativistic, ideal, magnetohydrodynamic, collimated outflows (jet and winds) from magnetized accretion disks around compact objects. The magnetic field extracts angular momentum from the disk, accelerates the outflows perpedicular to the disk, and provides collimation at large distances. The terminal outflow velocities are of the order of or greater than the rotational velocity of the disk at the base of the flow. When a nonzero electric current flows along the jet, the outflow radius oscillates with axial distance, whereas when the total electric current is zero (with the return current flowing across the jet's cross section), the outflow radius increase to a maximum and then decreases. The method can also be applied to relativistic outflows.
Contopoulos, J.↗
Magnetically driven relativistic jets and winds: Exact solutions
We present self-consistent solutions of the full set of ideal MHD equations which describe steady-state relativistic cold outflows from thin accretion disks. The magnetic field forms a spiral which is anchored in the disk, rotates with it, and accelerates the flow out of the disk plane. The collimation at large distances depends on the total amount of electric current that flows along the jet. We considered various distributions of electric current and derived the result that in straight jets which extend to infinite distances, a strong electric current flows along their axis of symmetry. The asymptotic flow velocities are of the order of the initial rotational velocity at the base of the flow (a few tenths of the speed of light). The solutions are applied to both galactic (small-scale) and extragalactic (large-scale) jets.
Contopoulos, J.↗
Exact Solutions for Sound Radiation from a Circular Duct
This paper presents a method of evaluation of Wiener-Hopf technique solutions for sound radiation from an unflanged circular duct with infinitely thin duct wall, including mean flows.
Cho, Y. C.↗
Exact Solutions for Sound Radiation from a Circular Duct
This paper presents a method of evaluation of Wiener-Hopf technique solutions for sound radiation from an unflanged circular duct with infinitely thin duct wall, including mean flows.
Cho, Y. C.↗
Exact Solutions to Category 1, Problem 3
The goal of this problem was to provide a detailed study of the accuracy of boundary treatments with a range of incidence angles including shear and a sonic point.
Hagstrom, Thomas↗
Exact Solutions of Equations of Gas Dynamics
This document presents equations for the two-dimensional stationary problem of gas dynamics, and uses them to derive other equations, including equations for vorticity.
Kiebel, I. A.↗